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  4. If f: A arrow B is an injective mapping such that f ( i ) ≠ i and A = 1,2,3,4 B = 1,2,3,4,5 then number of such mapping are

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Q. If $f : A \rightarrow B$ is an injective mapping such that $f ( i ) \neq i$ and $A =\{1,2,3,4\}, B =\{1,2,3,4,5\}$ then number of such mapping are

Relations and Functions - Part 2

Solution:

${ }^5 C _4 \cdot 4 !-\left[{ }^4 C _1 \times{ }^4 C _3 \times 3 !-{ }^4 C _2 \times{ }^3 C _2 \times 2 !+{ }^4 C _3 \cdot{ }^2 C _1 \cdot 1-{ }^4 C _4\right]$
$120-96+36-8+1 \Rightarrow 24+28+1 \Rightarrow 53$